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Summation and Square

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The values (in thousands of dollars) of cars owned by six persons are 13, 9, 3, 28, , and 16.

Where, X1 = 13, X2 = 9, X3 = 3, X4 =28, X5 = 7, X6 = 16

Calculate:

a. ΣX b. ΣX c. (Σ X)

Net present value & capital budgeting

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1) Assume a 3 year sports contract with the following provisions:
– $1,400,000 signing bonus
– $2,500,000 per year for 3 years
– 10 years of deferred payments of $1,250,000 per year beginning in year 4
– Other bonus provisions that total as mush as $750,000 per year for the 3 years of the contract.

Assume the player has a 60% probability of receiving the bonuses each year, that that he signed the contract on Jan 1, 2002. Use the exepected value of the bonuses as incremental cash flows. Assume that expected cash flows are discounted at 12.36%. There are no taxes for the sake of this problem. The signing bonus was paid on Jan 1, 2002. The salary and other bonuses are paid at the end of the year. What was the present value of this contract in January when it was signed?

2) A company is considering investing in a machine to produce computer keyboards. The price of the machine will be $400,000 and its economic life is 5 years. The machine will be fully depreciated by the straight line method. The machine will produce 10,000 keyboards each year. The price of each keyboard will be $40 in the first year and will increase by 5% per year. The production cost per keyboard will be $20 in the first year and will increase by 10% per year. The corporate tax rate for the company is 34%. If the discount rate is 15%, what is the net present value of the investment?

3) Shoe-tek is a leading manufacturer of running shoes. With the baby boomers getting older, they realized the potential market in shoes speciically designed for walking rather than running. Market research suggests that the walking shoe market will be $100 million and Shoe-tek could capture 20% of this market. However, it is estimated that 10% of Shoe-tek’s current sales of running shoes are already being used by baby-boomers for walking. If Shoe-tek introduces a walking shoe, half of these customers would switch from Shoe-tek’s running shoes to walking shoes. Shoe-tek has already spent $10 million on R&D for its running shoes and could leverage this and produce a totally new walking shoe for an additional $1 million in R&D. Shoe-tek would also ned to construct an extension to their warehouse to accomodate the additional materials and inventory. This extension would cost $1 million. If annual revenues for Shoe-tek are $80 million, what is the amount to use as the annual sales figure when evaluating this project? Why?

4) A new company producing lamps projected unit sales of their lamps to be 5,000 in the first year, with growth of 15% each year for the next 5 years. Production of these lamps will require $28,000 in net working capital to start, and additional net working capital investments each year equal to 40% of the projected sales increase for that year. Total fixed costs are $75,000 per year, variable production costs are $20 per unit, and the unites are priced at $45 each. The equipment needed to begin production will cost $60,000. The equipment will be depreciated using a straight-line method over a 5 year lkife and is not expected to have a salvage value. The effective tax rate is 34% and the required rate of return is 25%. What is the net present value of this project?

Your mail-order company advertises that it ships 90% of its orders within three working days

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Your mail-order company advertises that it ships 90% of its orders within three working days. You select a simple random sample of 100 of the 5000 orders received in the past week for an audit. The audit reveals that 86 of these were shipped on time. If the company really ships 90% of its orders on time, what is the probability that 86 or fewer in a simple random sample of 100 orders are shipped on time?

Normal approximation to binomial variable.

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Nathan wants to approximate a binomial probability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95

Can Nathan use the normal curve area to approximate a binomial probability?

A citizen’s action committee against nuclear power is comprised of 4 Democrats, 8 Republicans, and 3 Conservatives. If one person is randomly selected from this committee:

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1). A citizen’s action committee against nuclear power is comprised of 4 Democrats, 8 Republicans, and 3 Conservatives. If one person is randomly selected from this committee:

a. find the probability of selecting a Democrat.
b. find the probability of selecting a Democrat or a Republican.

2). An automobile manufacturer has a new model that they claim gets at least 27 miles per gallon. A consumer testing agency selects 50 of these cars and finds that the sample mean is 25 miles per gallon and the variance for this sample is 9 miles per gallon. Is the manufacturer’s claim accurate? (alpha =
0.05)

3). In a certain college, the men play various sports in the following proportions:
– Football = 60% of all men – Basketball = 50% of all men
– Both Football and Basketball = 30% of all men

If a man is randomly selected for an interview, what is the chance he will:
a. Play football or basketball?
b. Play neither sport?

A survey of 400 customers was completed in an attempt to measure the number of cups of coffee ordered during business hours versus those ordered during non-business (pleasure) hours. They also recorded how many items were purchased during the transaction.

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A survey of 400 customers was completed in an attempt to measure the number of cups of coffee ordered during business hours versus those ordered during non-business (pleasure) hours. They also recorded how many items were purchased during the transaction. Results are as follows:

Customer 0 extra 1 extra 2 extra 3 or more Total
Business 50 60 30 10 150
Pleasure 20 80 90 60 250
Total 70 140 120 70 400

1. What is the probability that a customer orders exactly 2 extra items?
2. What is the probability that a customer who responded to the survey was a business customer?
3. What is the probability that a customer ordered fewer than 2 extra items?
4. What is the probability that a customer visited during business hours or ordered exactly 1 extra item?

 
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